A328195 Maximum length of a divisibility chain of consecutive divisors of n greater than 1.

0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 2, 1, 2, 2, 4, 1, 2, 1, 3, 2, 2, 1, 2, 2, 2, 3, 3, 1, 2, 1, 5, 2, 2, 2, 2, 1, 2, 2, 3, 1, 2, 1, 3, 2, 2, 1, 2, 2, 2, 2, 3, 1, 2, 2, 3, 2, 2, 1, 2, 1, 2, 2, 6, 2, 2, 1, 3, 2, 2, 1, 2, 1, 2, 2, 3, 2, 2, 1, 3, 4, 2, 1, 2, 2, 2, 2, 4, 1, 2, 2, 3, 2, 2, 2, 2, 1, 2, 3, 3, 1, 2, 1, 4, 2

Offset: 1

Author

Gus Wiseman, Oct 14 2019

Keywords

• nonn

Comments

Also the maximum length of a divisibility chain of consecutive divisors of n less than n.

The divisors of n (except 1) are row n of A027749.

Examples

			The divisors of 272 greater than 1 are {2, 4, 8, 16, 17, 34, 68, 136, 272}, with divisibility chains {{2, 4, 8, 16}, {17, 34, 68, 136, 272}}, so a(272) = 5.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Allowing 1 as a divisor gives A328162.

Forbidding n as a divisor of n gives A328194.

Positions of 1's are A000040 (primes).

Indices of terms greater than 1 are A002808 (composite numbers).

The maximum run-length of divisors of n is A055874(n).

Cf. A000005, A033676, A060775, A163870, A328026, A328161, A328171.

Programs

Mathematica

Table[If[n==1,0,Max@@Length/@Split[DeleteCases[Divisors[n],1],Divisible[#2,#1]&]],{n,100}]

PARI

A328195(n) = if(1==n, 0, my(divs=divisors(n), rl=0,ml=1); for(i=2,#divs,if(!(divs[i]%divs[i-1]), rl++, ml = max(rl,ml); rl=1)); max(ml,rl)); \\ Antti Karttunen, Dec 07 2024

Extensions

Data section extended up to a(105) by Antti Karttunen, Dec 07 2024